All graphs with a Hamiltonian path are included in this count. The smallest n for which a graph with n vertices satisfies this property and does not have a Hamiltonian path is n=5.
Table of n, a(n) for n=1..7.
Sequence in context: A258830 A002484 A280102 * A115082 A020105 A347071
Adjacent sequences: A277683 A277684 A277685 * A277687 A277688 A277689
Caleb Ji, Sam Heil, Oct 26 2016